Effective heat redistribution in specific directions is vital for advanced thermal management, significantly enhancing device performance by optimizing spatial heat configurations. We have designed and fabricated a hierarchical fibrous membrane that enables precise heat directing. By integrating hierarchical structure design with the anisotropic thermal conductivity of two-dimensional (2D) materials, we developed a fibrous membrane for anisotropic heat transfer. Such a structure is fabricated by aligning a 1D structured fiber in the 2D plane to achieve anisotropy at each scale level. The fiber units, where 2D nanosheets circumferentially and axially aligned, achieved a high axial thermal conductivity of 16.8 W·m-1·K-1 and advanced heat directing ability, confirmed by characterizations and simulations. The assembled membrane demonstrated an exceptional tensile strength (365 MPa) and high thermal conductivity (10.5 W·m-1·K-1) along the fiber axis. Our membranes are seen as a refined model for thermal management materials, combining the benefits of heat spreaders and thermal interface materials, thus being proficient in directing heat along programmed pathways. A practical wireless charging cooling demonstration illustrated this. Our methodology also proved versatile with different 2D fillers and various geometries. This research presents a method to achieve precise heat directing at the material's level, facilitating the systematic design of thermal management in electronics.